Towards the Green-Griffiths-Lang conjecture

The Green-Griffiths-Lang conjecture stipulates that for every projective variety X of general type over C, there exists a proper algebraic subvariety of X containing all non constant entire curves f : C $\rightarrow$ X. Using the formalism of directed varieties, we prove here that this assertion holds true in case X satisfies a strong general type condition that is related to a certain jet-semistability property of the tangent bundle TX . We then give a sufficient criterion for the Kobayashi hyperbolicity of an arbitrary directed variety (X,V). This work is dedicated to the memory of Professor Salah Baouendi.Comment: version 2 has been expanded and improved (15 pages

Variable frequency microwave (VFM) processing facilities and application in processing thermoplastic matrix composites

Microwave processing of materials is a relatively new technology advancement alternative that provides new approaches for enhancing material properties as well as economic advantages through energy savings and accelerated product development. Factors that hinder the use of microwaves in materials processing are declining, so that prospect for the development of this technology seem to be very promising. The two mechanisms of orientation polarisation and interfacial space charge polarisation, together with dc conductivity, form the basis of high frequency heating. Clearly, advantages in utilising microwave technologies for processing materials include penetration radiation, controlled electric field distribution and selective and volumetric heating. However, the most commonly used facilities for microwave processing materials are of fixed frequency, e.g. 2.45 GHz. This paper presents a state-of-the-art review of microwave technologies, processing methods and industrial applications, using variable frequency microwave (VFM) facilities. This is a new alternative for microwave processing

On the cohomology of pseudoeffective line bundles

The goal of this survey is to present various results concerning the cohomology of pseudoeffective line bundles on compact K{\"a}hler manifolds, and related properties of their multiplier ideal sheaves. In case the curvature is strictly positive, the prototype is the well known Nadel vanishing theorem, which is itself a generalized analytic version of the fundamental Kawamata-Viehweg vanishing theorem of algebraic geometry. We are interested here in the case where the curvature is merely semipositive in the sense of currents, and the base manifold is not necessarily projective. In this situation, one can still obtain interesting information on cohomology, e.g. a Hard Lefschetz theorem with pseudoeffective coefficients, in the form of a surjectivity statement for the Lefschetz map. More recently, Junyan Cao, in his PhD thesis defended in Grenoble, obtained a general K{\"a}hler vanishing theorem that depends on the concept of numerical dimension of a given pseudoeffective line bundle. The proof of these results depends in a crucial way on a general approximation result for closed (1,1)-currents, based on the use of Bergman kernels, and the related intersection theory of currents. Another important ingredient is the recent proof by Guan and Zhou of the strong openness conjecture. As an application, we discuss a structure theorem for compact K{\"a}hler threefolds without nontrivial subvarieties, following a joint work with F.Campana and M.Verbitsky. We hope that these notes will serve as a useful guide to the more detailed and more technical papers in the literature; in some cases, we provide here substantially simplified proofs and unifying viewpoints.Comment: 39 pages. This survey is a written account of a lecture given at the Abel Symposium, Trondheim, July 201

Effective algebraic degeneracy

We prove that any nonconstant entire holomorphic curve from the complex line C into a projective algebraic hypersurface X = X^n in P^{n+1}(C) of arbitrary dimension n (at least 2) must be algebraically degenerate provided X is generic if its degree d = deg(X) satisfies the effective lower bound: d larger than or equal to n^{{(n+1)}^{n+5}}

The home team advantage gives football referees something to ruminate about

Observation suggests that referees significantly contribute to the home team advantage in football. The atmosphere created by the home team fans is thought to be the major contributing factor, but the extent of this influence is dependent on the referee. The Decision-Specific Reinvestment Scale was developed to identify those individuals susceptible to disrupted decision making under pressure as a result of their tendency to overinvolve consciousness in decision making (Decision Reinvestment) or as a result of their tendency to ruminate upon poor decisions made in the past (Decision Rumination). We asked qualified referees to make a series of video-based decisions to examine whether the home team advantage effect was associated with a high or low tendency for Decision Reinvestment or Decision Rumination. We showed that referees categorized as high Decision Ruminators disproportionately made decisions in favour of the home team. The tendency to ruminate upon poor decisions may help explain some of the variance in the home team advantage effect shown by different referees. We conclude that aspects of personality should be considered in the development of training programs designed to improve and standardise football refereeing.published_or_final_versio

Classification of the Lie bialgebra structures on the Witt and Virasoro algebras

We prove that all the Lie bialgebra structures on the one sided Witt algebra W1, on the Witt algebra W and on the Virasoro algebra V are triangular coboundary Lie bialgebra structures associated to skew-symmetric solutions r of the classical Yang-Baxter equation of the form r = a ∧ b. In particular, for the one-sided Witt algebra W1 = Der k[t] over an algebraically closed field k of characteristic zero, the Lie bialgebra structures discovered in Michaelis (Adv. Math. 107 (1994) 365-392) and Taft (J. Pure Appl. Algebra 87 (1993) 301-312) are all the Lie bialgebra structures on W1 up to isomorphism. We prove the analogous result for a class of Lie subalgebras of W which includes W1. © 2000 Elsevier Science B.V. All rights reserved

On infectious models for dependent default risk

Modeling dependent defaults is a key issue in risk measurement and management. In this paper, we introduce a Markovian infectious model to describe the dependent relationship of default processes of credit entities. The key idea of the proposed model is based on the concept of common shocks adopted in the insurance industry. We compare the proposed model to both one-sector and two-sector models considered in the credit literature using real default data. A log-likelihood ratio test is applied to compare the goodness-of- fit of the proposed model. Our empirical results reveal that the proposed model outperforms both the one-sector and two-sector models. © 2011 IEEE.published_or_final_versionThe 4th International Joint Conference on Computational Sciences and Optimization (CSO 2011), Yunnan, China, 15-19 April 2011. In Proceedings of the 4th CSO, 2011, p. 1196-120

Section Extension from Hyperbolic Geometry of Punctured Disk and Holomorphic Family of Flat Bundles

The construction of sections of bundles with prescribed jet values plays a fundamental role in problems of algebraic and complex geometry. When the jet values are prescribed on a positive dimensional subvariety, it is handled by theorems of Ohsawa-Takegoshi type which give extension of line bundle valued square-integrable top-degree holomorphic forms from the fiber at the origin of a family of complex manifolds over the open unit 1-disk when the curvature of the metric of line bundle is semipositive. We prove here an extension result when the curvature of the line bundle is only semipositive on each fiber with negativity on the total space assumed bounded from below and the connection of the metric locally bounded, if a square-integrable extension is known to be possible over a double point at the origin. It is a Hensel-lemma-type result analogous to Artin's application of the generalized implicit function theorem to the theory of obstruction in deformation theory. The motivation is the need in the abundance conjecture to construct pluricanonical sections from flatly twisted pluricanonical sections. We also give here a new approach to the original theorem of Ohsawa-Takegoshi by using the hyperbolic geometry of the punctured open unit 1-disk to reduce the original theorem of Ohsawa-Takegoshi to a simple application of the standard method of constructing holomorphic functions by solving the d-bar equation with cut-off functions and additional blowup weight functions